Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#15668533 |
| Fitting, derived, Hall | C52×C9×C29 ⋊ C4 |
| Hall | C52×C29 ⋊ Dic9 |
| Hall | C9×C29 ⋊ #1042 |
| Hall | C52×C9 ⋊ #1181 |
| Sylow | C29 ⋊ C9⋊#1042 |
| Sylow | C52 ⋊ C9⋊#1181 |
| Sylow | C9 ⋊ #15668533 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C9×C29 | C4 |
| Frattini | C3 | C3⋊#15668533 |
| socle | C3×C52×C29 | Dic3 |
| prime radical | C3×C5×D145 | D3 |
| cosocle | C5×C9×D145 | C2 |
| LCS | G ▷ C52×C9×C29 | |
| UCS | C1 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5220 |
Polycyclic presentation:
2^2,3,5^2,29,3|a^2=b,c^3=g^2,c^a=c^2g,d^a=d^2,e^a=e^4,f^a=f^12,g^a=g^2,d^b=d^4,f^b=f^281668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 196);